Phase diagram of one-, two-, and three-dimensional quantum spin systems derived from entanglement properties

TL;DR

This paper investigates the phase diagrams of 1D, 2D, and 3D quantum spin-1/2 models using bipartite entanglement from tensor network ground state representations, revealing characteristic features across dimensions.

Contribution

It introduces a method to analyze phase diagrams of quantum spin systems in multiple dimensions via bipartite entanglement derived from tensor networks.

Findings

Identifies phase boundaries using entanglement measures.

Demonstrates the effectiveness of tensor network methods in higher dimensions.

Provides detailed phase diagrams for Ising, XY, and XXZ models.

Abstract

We study the bipartite entanglement per bond to determine characteristic features of the phase diagram of various quantum spin models in different spatial dimensions. The bipartite entanglement is obtained from a tensor network representation of the ground state wave-function. Three spin-1/2 models (Ising, XY, XXZ, all in a transverse field) are investigated. Imaginary-time evolution (TEBD in 1D, `simple update' in 2D and 3D) is used to determine the ground states of these models. The phase structure of the models is discussed for all three dimensions.